In this paper, we compare the proposed algorithm with five traditional algorithms from the computational complexity and memory complexity aspects, including the AMP algorithm [1]}, the learned AMP (LAMP) algorithm [2]}, the learned vector AMP (LVAMP) algorithm [2]}, the fast iterative shrinkage-thresholding algorithm (FISTA) [4]} which is a classical optimization algorithm to minimize convex functions, and the OMP algorithm which is a greedy algorithm proposed in [5]}. It can be seen in Table REF  that the computational complexity scalings of FAT-DL is superior to the traditional algorithms, implying its lower complexity in the high dimensional regime. Note that, an \(r^e \times r^e\)  SVD is performed for dimension reduction, whose computational complexity in the worst case is \(\mathcal {O}(\min (L,M)^2)\) . For sparse recovery, since \(r^e \le K\)  and SVD only
needs to be calculated once at each time slot before the start of iteration, this step is not numerically expensive. Moreover, the memory complexity of the proposed FAT-DL algorithm is lower than that of the LAMP and LVAMP algorithms in mMTC, which is an advantageous feature for massive device detection problems.
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